LogFiles folder for Azure Web Sites contains details of almost and everything of all the related logs from IIS logs, Detailed Error Logs, FREB logs, Event Logs, Application Logs, KUDS Logs (deployment and traces) and more.
This would be the first place to look at when your application running on Azure Web Sites has any issues. Below are few ways to download the LogFiles to your local machine for easy access.
Download using KUDU console:
Browse to the KUDU console at https://<sitename>.scm.azurewebsites.net/DebugConsole where <sitename> should be replaced by your Azure Web Site name
Go to "LogFiles" folder and this would contain all related logs for your site, if they are enabled. The "LogFIles" folder can also be downloaded by clicking on the down arrow image.
Download using FTP:
FTP to your website using FTP clients like FileZilla or other tools
FTP credentials for your website can be found in the Dashboard of your Azure Web Site. The user name is the "FTP USER" highlighted below and the format is usually like websitename\LiveID